Dynamic Programming
Dynamic programming is a method for solving complex problems by breaking them down into simpler overlapping subproblems, solving each subproblem only once, and storing their solutions to avoid redundant computations. It is widely used in optimization, computer science, and mathematics to efficiently compute solutions for problems like shortest paths, resource allocation, and sequence alignment. The approach typically involves recursion, memoization, or tabulation to build up solutions from smaller instances.
Developers should learn dynamic programming when dealing with optimization problems that exhibit optimal substructure and overlapping subproblems, such as in algorithms for the knapsack problem, Fibonacci sequence calculation, or edit distance in string processing. It is essential for competitive programming, software engineering interviews, and applications in bioinformatics, economics, and operations research where brute-force solutions are computationally infeasible.